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Journal of Physics A Mathematical and General

Critical dynamics of the one-dimensional generalised kinetic Ising model

Y Achiam

Published Apr 1, 1980• 10 citations
Publisher

Abstract

A time-dependent real-space renormalisation group is used to show that all the one-dimensional kinetic Ising models with transition rate that depends on nearest neighbours only belong to the same universality glass of the critical dynamics.
DOI
10.1088/0305-4470/13/4/004

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A plausible argument using the concepts of dynamic renormalisation group is used to derive the dynamical exponent z of the one-dimensional q=2, 3 and 4 Potts and four-state clock models. The exact result (z=2) for the Ising model with Glauber dynamics is recovered and in addition the authors find that the q=3, 4 Potts and four-state clock models belong to the same universality class. Moreover they find that z=3.05+or-0.1 for the (q=2) Potts model with Kawasaki dynamics in agreement with the z=4- eta prediction of Halperin, Hohenberg and Ma (1974). A simple qualitative derivation is also given.